ALICE rf project meeting

reelingripebeltUrban and Civil

Nov 15, 2013 (3 years and 6 months ago)

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1

ALICE rf project meeting




Kai Hock, Cockcroft / Liverpool


19 May 2008

2

Status


Aug
-

Dec 07: 4GLS beam loading (Hywel, Yuri)


Worked through Wiedemann’s chapter, Perry Wilson’s report on rf system


Reproduced simulation on 4GLS beam loading (Sakanaka ERL07)


Report on beam loading


basics, 4GLS



Feb 08: ALICE rf control


new phase


Mar 08: ALICE


intro to rf system (Andy)


Apr 08:


Contacted, received paper, suggestions from Tom Powers


Looking up references: rf feedback, energy recovery theory, …


Started learning rf control hardware, set up by Andy


Idea: connect cavity / stretched wire to simulate beam loading


May 08


Simulation on klystron power


with energy recovery ?


Set up stretched wire experiments ?


3

RF system theory


Feedback control


experiments



Stefan Simrock’s LLRF lectures


Papers on ELBE rf system



Beam loading


Wiedemann’s textbook, Wilson’s SLAC report (beam loading)


Sakanaka’s ERL07 paper (4GLS simulation)



Energy recovery linac


Thomas Schilcher’s PhD thesis (microphonics, Lorentz detuning)


Lia Merminga’s 2001 USPAS lectures (beam loading in ERL)


Tom Power’s paper

4

Deciphering Tom’s paper


Why / how does energy recovery happen?


What are r/Q,

Q
L
, Q
0
,

,

f
S
,

B
, …
?


How does the klystron power equation come about?


What are microphonics, Lorentz detuning, ponderomotive
effects, vector sum, … ?


Why are we interested in detuning? What are mechanical
tuners?


Why is detuning measured by the Klystron
-
cavity phase
difference?


When Q
L

is optimized, what exactly is minimised or
maximised? The klystron power?


Why is incomplete energy recovery needed? How does
this compress the energy spread?


What are page 2, page 3, page 4 and page 5 about?

Questions from a complete beginner

5

Finding Answers

Why Energy Recovery

“ … the beam
-
induced voltage in a cavity is the same
whether or not a generator voltage component is present.”

(Wilson 1991,

sect. 6.1 The Fundamental Theorem of Beam Loading )

The beam induced voltage is always negative.


Therefore, if a bunch enters at the opposite phase
of the cavity field, it will increase the amplitude of
the field.


This gives energy to the cavity.

(Sakanaka ERL07)

6

Finding Answers

Shunt Impedance

(Wiedemann 2003)

A full calculation from Maxwell’s equations for pillbox cavity:

7

Finding Answers

Many equations come from this !

(Wiedemann 2003)

8

Finding Answers

r/Q,

Q
L
, Q
0
,

,

B
, …

(Wiedemann 2003)

This
models


the behaviour of

the cavity voltages.

Mostly using

equations from

simple harmonic

oscillator.

9

Finding Answers

How the beam affects the cavity voltage

All voltages defined along the axis of cavity (beam path):



generator (klystron) voltage V
g


beam induced voltage V
b


and resultant cavity voltage V
c



Assuming all sinusoidal, they can be related by a phasor diagram.

(Wilson 1991)

10

Finding Answers

The klystron power equation

2 2
2
0 0
(1 )
1 cos tan sin
4
c L L
g b b
L c c
V I R I R
P
R V V

 

 
   

 
   
 
   
   
 
 
r/Q,

Q
L
, Q
0
,

, … are measured

by fitting to the equivalent circuit model

The klystron power can be calculated

from these parameters using the model.

Merminga (2001) explains how to get this:

Steps are easy once we have worked from

Wiedemann and Wilson.

The main equation

in Tom’s paper

11

Finding Answers

Energy recovery calculations


ERL Injector and Linac:



f
m
=25 Hz, Q
0
=1x10
10

, f
0
=1300 MHz, I
0
=100 mA, V
c
=20 MV/m, L=1.04 m,
R
a
/Q
0
=1036

ohms per cavity



ERL linac: Resultant beam current, I
tot

= 0 mA (energy recovery)


and

opt
=385


Q
L
=2.6x10
7



P
g

= 4 kW per cavity.



ERL Injector: I
0
=100 mA and

opt
= 5x10
4

!


Q
L
= 2x10
5



P
g

= 2.08 MW
per cavity!


Note: I
0
V
a

= 2.08 MW


optimization is entirely dominated by beam loading.

Nice examples from Merminga (2001)

12

Finding Answers

Microphonics, Lorentz Force, Vector Sum

(Schilcher 1998)

Revelation !

13

Finding Answers

What exactly is being optimized?

(Liepe PAC05)

The klystron power, of course !

14

Finding Answers

Ponderomotive force

15

Finding Answers

Page 2 of Tom’s paper

One bunch at a time?

10
o

165
o

1
st

pass

2
nd

pass

I
B

?

Shall try to do this next

16

Experiments


References on Feedback control


Stefan Simrock’s LLRF lectures


Papers on ELBE rf system



Andy’s Rossendorf control unit


Connect control system to standalone cavity


Stretched wire measurements with short pulses



Ideas for experiments


For learning about rf control


For modelling of beam loading / energy recovery